Related papers: Unique continuation for a gradient inequality with…

In this article, we study the quantitative uniqueness of solutions to second order elliptic equations with singular lower order terms. We quantify the strong unique continuation property by estimating the maximal vanishing order of…

In this paper we study the local behavior of a solution to the Lam\'e system with \emph{Lipschitz} coefficients in dimension $n\ge 2$. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies…

In this work, we investigate the quantitative estimates of the unique continuation property for solutions of an elliptic equation $\Delta u = V u + W_1 \cdot \nabla u + \hbox{div} (W_2 u)$ in an open, connected subset of $\mathbb{R}^d$,…

We derive the unique continuation property of a class of semi-linear elliptic equations with non-Lipschitz nonlinearities. The simplest type of equations to which our results apply is given as $-\Delta u = |u|^{\sigma-1} u$ in a domain…

Asymptotics of solutions to relativistic fractional elliptic equations with Hardy type potentials is established in this paper. As a consequence, unique continuation properties are obtained.

In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong…

We prove quantitative unique continuation results for solutions of $\Delta w - k^2 w = V w + W\cdot \nabla w$ in a neighborhood of infinity, where $k > 0$, and $V$ and $W$ are complex-valued decaying potentials that satisfy $|V(x)| \lesssim…

We prove quantitative unique continuation results for solutions of $-\Delta u + W\cdot \nabla u + Vu = \lambda u$, where $\lambda \in \mathbb{C}$ and $V$ and $W$ are complex-valued decaying potentials that satisfy $|V(x)| \lesssim \langle…

This article is concerned with the unique continuation property of a forward differential inequality abstracted from parabolic equations proposed on a convex domain $\Omega$ prescribed with some regularity and growth conditions. Our result…

In this note we prove the strong unique continuation property at the origin for the solutions of the parabolic differential inequality \[ |\Delta u - u_t| \leq \frac{M}{|x|^2} |u|, \] with the critical inverse square potential. Our main…

We prove a scale-free quantitative unique continuation estimate for the gradient of eigenfunctions of divergence-type operators, i.e. operators of the form $-\mathrm{div}A\nabla$, where the matrix function $A$ is uniformly elliptic. The…

We obtain a vanishing result for solutions of the inequality $|\Delta u|\le q_1|u|+q_2|\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is…

A differential operator $T$ satisfies the $L^2$-unique continuation property if every $L^2$-solution of $T$ that vanishes on an open subset vanishes identically. We study the $L^2$-unique continuation property of an operator $T$ acting on a…

We establish new, optimal gradient continuity estimates for solutions to a class of 2nd order partial differential equations, $\mathscr{L}(X, \nabla u, D^2 u) = f$, whose diffusion properties (ellipticity) degenerate along the \textit{a…

In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a domain, we investigate the unique…

Unique continuation principles are fundamental properties of elliptic partial differential equations, giving conditions that guarantee that the solution to an elliptic equation must be uniformly zero. Since finite-element discretizations…

We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and…

In this work we analyse the functional ${\cal J}(u)=\|\nabla u\|_\infty$ defined on Lipschitz functions with homogeneous Dirichlet boundary conditions. Our analysis is performed directly on the functional without the need to approximate…

Let $u: \Omega \subset \mathbb C^n \to \mathbb C^m$, for $n \geq 2$ and $m \geq 1$. Let $1 \leq p \leq 2$, and $2(2n)^2 -1 \leq q < \infty$ such that $\displaystyle \frac{1}{p} + \frac{1}{p'} = 1$ and $\displaystyle \frac{1}{p} -…

The question of unique continuation of harmonic functions in a domain $\Omega$ $\subset$ R d with boundary $\partial$$\Omega$, satisfying Dirichlet boundary conditions and with normal derivatives vanishing on a subset $\omega$ of the…